Charged particle accelerators used in oil-well logging generally produce secondary beams of uncharged particles, such as neutrons and photons, which effectively penetrate the borehole formation. For example, FIG. 1 shows a schematic diagram of a prior art neutron generator 10. The neutron generator 10 comprises a metal pressure vessel 12 that houses a Cockcroft-Walton (C-W) voltage multiplier 14. The C-W multiplier comprises a circuit of discrete elements that are hard wired together in a ladder circuit. The C-W multiplier is powered by a voltage supply 16 that energizes a transformer 18 within the metal pressure vessel 12. The C-W multiplier 14 multiplies the power from the transformer 18 as described below concerning FIGS. 2 and 3. The output of the C-W multiplier 14 biases the ring 20 of an acceleration tube 22 and an ion target 24. Thus, ions from an ion source 26 are accelerated toward the target 24 in a known manner. A resistor 28 protects the acceleration tube 22 from current surges.
FIG. 2 illustrates a two stage Cockcroft-Walton voltage multiplier. The Cockcroft-Walton voltage multiplier 14 essentially consists of an oscillating voltage drive source 16 (not necessarily sinusoidal), two series capacitor banks 30, 32, and a diode matrix 34 which interconnects the capacitors. Capacitors C1 and C3 represent an AC capacitive bank 30 and capacitors C2 and C4 represent a DC capacitive bank 32. Diodes D1 through D4 are high voltage rectifiers. On positive peaks of the source voltage, diodes D1 and D3 conduct and D2 and D4 are reverse biased (off). At this time, capacitors C1 and C3 are charged. On negative voltage peaks D1 and D3 are off and D2 and D4 conduct, charging C2 and C4.
FIG. 3 shows a PSpice simulation of the circuit of FIG. 2. All components are assumed to be ideal. The circuit is excited by the 15 kV peak-voltage sinusoidal source, with a 1 ohm source impedance 36. Current through a 12M.OMEGA. load resistor 28 is approximately 5 mA. Voltage traces from points V(1) through V(5) referenced to ground are shown. The cycle of FIG. 3 occurs after charging transients have subsided. Trace V(1) is the ladder excitation voltage. At time A of FIG. 3, diodes D2 and D4 are reverse biased (off) and diodes D1 and D3 begin to conduct. While current is flowing through D1 into C1, point V(2) is at a voltage extremum of zero. The voltage at V(3) is also at an extremum and is equal to V(4). As soon as the source reaches its peak voltage, current ceases to flow through D1 and D3. From this point until time B, all diodes are reversed biased and no charge flows between capacitor banks. Charge continues to bleed off from C2 and C4 though the load resistor 28, causing voltages V(4) and V(5) to droop. Also at time B, diodes D2 and D4 begin to conduct, transferring charge from capacitors C1 and C3 to C2 and C4. Charging continues until the source reaches its peak negative voltage at time C. On each half cycle of the voltage signal, the resulting charge is ratcheted up successive stages of the ladder to the acceleration tube 22.
FIG. 3 illustrates that all nodes on the AC capacitor bank 30 have an oscillatory component essentially equal to that of the source 16. The large ripple is one reason that the AC bank 30 is unsuitable to use for voltage grading around the acceleration tube 22. A more important reason for not attaching an acceleration tube to the AC bank 30 is the loss in ladder charging efficiency due to stray capacitances from the AC bank to ground. Stray capacitances from the DC bank 32 to ground actually aid charging efficiency.
Such an arrangement, however, results in a nonlinear field, especially at the end of the ladder toward the resistor 28. Any given dielectric is used optimally in a linear field, because all parts of the dielectric are stressed equally. At very high field strengths, electrostatic forces can reduce electrode spacing by deforming the dielectric, leading to breakdown. The problem is particularly severe in geometries where the dielectric is not constrained mechanically in all three dimensions. A major obstacle to increased neutron output, however, has been high voltage discharge within the neutron tube and in the surrounding insulation. Higher neutron output may be achieved through increased beam current but this has the disadvantages of decreased target lifetime and higher target power dissipation. The C-W multiplier 14 of the neutron generator 10 produces a radial field that is nonlinear, because the field is a function of the inverse of the radius.
Voltage dividers with one or two intermediate electrodes have been used in Van de Graaff accelerators to approximately linearize a radial field. The voltage dividers are, however, driven by a resistive voltage divider. Van de Graaff accelerators also use resistive voltage dividers to linearize the axial field. Single capacitive voltage dividers have been used to linearize radial fields to some degree in high voltage cable terminations. These capacitive dividers comprise single, passive (non-driven) dividers.